Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
Measurement Topic
This standard is reported on the report card in these quarters as follows:
1st Grade Students Learning 1st Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic: Demonstrates understanding of addition.
Report Card Measurement Topic: Demonstrates understanding of addition.
Kindergarten Students Learning 1st Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic: Demonstrates understanding of addition.
Report Card Measurement Topic: Demonstrates understanding of addition.
About the Math
Skills and concepts below are learning goals for this standard.
Explain that changing the order of the addends (numbers) does not change the sum using varied representations. (Quarter 1)
Explain that when adding three number in any order, the sum does not change (e.g., 2 + 3 + 1 = 5 + 1). (Quarter 3 and 4)
Represent properties of operations with equations.
Use properties of operations to add and subtract.
It is a focus for students to discover and apply the commutative and associative properties as strategies for solving addition problems.
The commutative property of addition tells us that the order of addends does not change the sum. It can help us find unknown facts. It can help us be more efficient. We might use dominoes to model the commutative property. We might use unifix or linker cubes. Ask students to show addition problems using unifix cubes or linker cubes. Say: "Show me 5 + 4 using two different colors". Students could show 5 red cubes and 4 blue cubes. Ask them to look at the bar and then turn it over so there are 4 blue cubes and 5 red cubes. Ask: So is 5 + 4 the same as 4 + 5? How do you know?
The associative property of addition tells us that the order of adding more than 2 addends does not matter. It also tells us that we can decompose an addend and rearrange the partial addends. This is useful for making computation more friendly. For example, in 7 + 5 we can decompose 5 into 3 + 2 and then add 7 + 3 + 2. The associative property begins in the 3rd quarter to support work with the basic fact sets in that quarter as well as addition with two-digit numbers.
IMPORTANT NOTE: Students do not need to memorize/recall the terms commutative or associative. As teachers, we must use the correct terminology. Also, the commutative property should not be called the "flip-flop" property or something else less formal. Students do not need to record the associative property with parenthesis. It is important for students to share, discuss, and compare their strategies as a class. First graders should be working with sums and differences less than or equal to 20 using the numbers 0 to 20.
Provide investigations that require students to identify and then apply a pattern or structure in mathematics. For example, pose a string of addition and subtraction problems involving the same three numbers chosen from the numbers 0 to 20, like 4 + 13 = 17 and 13 + 4 = 17. Students analyze number patterns and create conjectures or guesses. Have students choose other three number combinations and explore to see if the patterns work for all numbers 0 to 20. Students then share and discuss their reasoning. Be sure to highlight students’ uses of the commutative and associative properties and the relationship between addition and subtraction. Essential vocabulary for this standard includes: addition, add, subtraction, subtract, commutative, and associative property (online dictionaryLinks to an external site., HCPSS Vocabulary CardsDownload HCPSS Vocabulary Cards).
Progression of Standard within Grade 1
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Progression Throughout Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Explain that adding zero to any number does not change the number using varied representations. (Quarter 1)
Explain that changing the order of the addends (numbers) does not change the sum using varied representations. (Quarter 1)
Represent properties of operations with equations.
Use properties of operations to add and subtract.
Represent properties of operations with equations.
Use properties of operations to add and subtract.
Explain that when adding three number in any order, the sum does not change (e.g., 2 + 3 + 1 = 5 + 1). (Quarter 3 and 4)
Represent properties of operations with equations.
Use properties of operations to add and subtract.
*Revisit this standard through routines, independent practice, discussions, and other activities.
These tasks can be used with small group or whole group instruction.
Pick 8 students to come up and stand in a line in the front left of the room. Then pick 3 students to come and stand in the front right of the room. Ask "What is an equation I could write to find the total number of students standing up front?" Once they share write 8 + 3 on the board and have them help you figure out the total. Then have the SAME students just swap places (the 3 students go on the left and the 8 students go to the right). Ask "Did my total number of students standing in the front change?" and "What changed?" Write the new equation 3 + 8 = 11 on the board after they have discussed the swap of the groups. Keep doing various combinations of students until every student has a turn to come up front and they see that it does not matter which order we add in, the total amount of students stays the same. Explain this is called the commutative property of addition and write it on the board for them to practice saying. You can repeat this activity with 3 groups of students coming to the front to teach the associative property. Be intentional to try to make friendly numbers with 2 of the amounts and then add the other number on. ( making 5 pairs, making 10 pairs, doubles)
Write or print the digits 0-9 large on individual pieces of paper. Hand them out to students. Have the student who has 6 come up front and hold it and then have the student who has 4 to come up front on hold their sign. Ask "If I wanted to find the total of 6 and 4 what is an equation I could write?" Have a different student come up and write it on the board. Help the class practice counting on from 6 to find the total and have a student record it for the equation. Then have the students swap places and ask "what would be the equation now?" Have a student record the equation and then help the class count on from 4 to find the total of 10 to be the same. Keep practicing with different students coming up and swapping places to find the totals. Debrief "Does the sum stay the same when we swap the places of the addends?" When you are teaching the associative property you can practice the same way but have 3 students come up with digit signs and have them move around to practice counting on to see you can add in any order but giving specific combinations to move to make a friendly pair. (3+ 5 + 2, 4+ 1+ 6, etc.)
Give the students 20 two-color counters. Have them show 4 red and 3 yellow. Ask them to write an equation to match to show the total. Then have them switch the places so its 3 yellow and 4 red. Ask them to write the new equation and total. Keep practicing with various combinations as needed. Eventually have them build one problem (2 red, 5 yellow) write the equation and total and have them write the matching commutative equation without having to swap the counters around.
How would you describe the commutative property to someone from another planet?
Show me 2 different examples that proves the commutative property.
Why does the total stay the same, even though you are adding in a different order? (example 6+5=11 and 5+6=11) Use drawings and/or models to help explain.
Would you get the same sum if you had two blue buttons and three red buttons as you would if you had three blue buttons and two red buttons? Can you write the addition sentences that show that?
Laura had 5 fish. Her mother gave her 1 more. Laura’s brother Frank had 1 fish. Their mother gave Frank 5 more. Laura cried, “That’s not fair! He has more fish than I do!” Frank doesn’t agree. Who is correct? How you know?
I own a pet store. There are 9 dogs, 1 cat and 3 fish in the store. How many pets are in the store? What number sentence could you write to match this story problem? Where is 10 in this number sentence? What new number sentence could we write to match what we did?
Laura solved the following problem: 7 + 2 + 3 = 12 How do you decide which numbers to add together first? What “friendly” number combinations do you see? Will we get the same number if we solve it different ways?
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first(often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Print Resources
Book Thumbnail
Book Title
Grade
Pages
Teaching Student-Centered Mathematics
K-3
Equations with Number Patterns, Activity 3.1, Page 73 More Than Two Addends, Activity 3.3, Page 76
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
Apply properties of operations as strategies to add and subtract.3 Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)
Measurement Topic
The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.
First Grade Students Learning First Grade Standards by Measurement Topic
Use the links below to access a task for this standard as well as student work samples that are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.
Explain Changing Order of Addends Does Not Change Sum A